The sum of two numbers is $55$, and their difference is $5$. What are the two numbers?
Solution: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 55}$ ${x-y = 5}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 60 $ $ x = \dfrac{60}{2} $ ${x = 30}$ Now that you know ${x = 30}$ , plug it back into $ {x+y = 55}$ to find $y$ ${(30)}{ + y = 55}$ ${y = 25}$ You can also plug ${x = 30}$ into $ {x-y = 5}$ and get the same answer for $y$ ${(30)}{ - y = 5}$ ${y = 25}$ Therefore, the larger number is $30$, and the smaller number is $25$.